MHD mixed convection flow in a vertical lid-driven square enclosure including a heat conducting horizontal circular cylinder with Joule heating

Abstract

In the present numerical investigation we studied the effect of magnetohydrodynamic (MHD) mixed convection flow in a vertical lid-driven square enclosure including a heat conducting horizontal circular cylinder with Joule heating. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin's finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter (Hartmann number) Ha, Joule heating parameter J, Reynolds number Re and Richardson number Ri. The streamlines, isotherms, average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicated that the Hartmann number, Reynolds number and Richardson number have strong influence on the streamlines and isotherms. On the other hand, Joule heating parameter has little effect on the streamline and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.